Animating rotation with quaternion curves
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A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations
CA '95 Proceedings of the Computer Animation
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In a Riemannian manifold, generalised B-spline curves are piecewise C^~ curves defined by a generalisation of the classical Cox-de Boor algorithm, in which line segments are replaced by minimal geodesics. Their applications include rigid body motion planning and computer graphics. We prove that, like classical B-spline curves, they are C^1 at knots of multiplicity at most m-1, where m is the degree. We then compute the difference between their left and right (covariant) accelerations at knots of multiplicity at most m-2. Unlike classical B-spline curves, generalised B-spline curves are not in general C^2 at such knots